Weak invariant simulation and analysis of parameterized networks

Multi-process networks figure in many engineering applications such as communication networks, transportation networks, manufacturing and logistic systems, and computer hardware and software. Parameterized discrete event systems provide a convenient means of modeling such networks when the number of subprocesses is arbitrary, unknown or time-varying. Unfortunately, some key properties of these networks, such as nonblocking and deadlock-freedom, are undecidable. Moreover, mathematical tools supporting analysis of these networks are limited. This thesis introduces a novel mathematical notion, weak invariant simulation and proposes an efficient method to check whether a finite-state generator weakly invariantly simulates another finite-state generator with respect to a specific subalphabet. This new simulation relation is first used to define a tractable subclass of parameterized ring networks of isomorphic subprocesses in which deadlock-freedom is decidable. Within this framework, a procedure is given to determine the reachable deadlocked states of the network. The effectiveness of the procedure is demonstrated by the deadlock analysis of a version of the dining philosophers problem. To generalize the results on ring networks, we consider a network consisting of several linear parameterized sections but exhibiting a branching topology. To model these networks we introduce Generalized Parameterized Discrete Event Systems (GPDES). The difficulty in analysis of a GPDES is the fact that some of the subprocesses interact with several parameterized sections of the network. Hence the analysis proposed in this thesis involves careful study of interaction among different branches of the network. Here again, we use `weak invariant simulation' to limit the behavior of subprocesses of the network. Then we investigate interactions among different components of the network, using a dependency graph. The dependency graph is a directed graph developed to characterize reachable partial deadlocks caused by generalized circular waits in the proposed GPDES. Our results implicitly characterize reachable generalized circular waits as a language accepted by a finite automaton. Our framework allows for modeling and analysis of new parameterized problems. We investigated deadlock in a large-scale factory as an illustrative example

Non-Blockingness Verification of Bounded Petri Nets Using Basis Reachability Graphs -- An Extended Version With Benchmarks

In this paper, we study the problem of non-blockingness verification by tapping into the basis reachability graph (BRG). Non-blockingness is a property that ensures that all pre-specified tasks can be completed, which is a mandatory requirement during the system design stage. In this paper we develop a condition of transition partition of a given net such that the corresponding conflict-increase BRG contains sufficient information on verifying non-blockingness of its corresponding Petri net. Thanks to the compactness of the BRG, our approach possesses practical efficiency since the exhaustive enumeration of the state space can be avoided. In particular, our method does not require that the net is deadlock-free.Comment: This article is an extended version of the paper "C. Gu, Z. Ma, Z. Li and A. Giua. Non-blockingness verification of bounded Petri nets using basis reachability graphs. IEEE Control Systems Letters, doi:10.1109/LCSYS.2021.3087937, 2021" with benchmark

Verification of Nonblockingness in Bounded Petri Nets With Minimax Basis Reachability Graphs

This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We construct a structure, called minimax basis reachability graph (minimax-BRG): it provides an abstract description of the reachability set of a net while preserving all information needed to test if the net is blocking. We prove that a bounded deadlock-free Petri net is nonblocking if and only if its minimax-BRG is unobstructed, which can be verified by solving a set of integer constraints and then examining the minimax-BRG. For Petri nets that are not deadlock-free, one needs to determine the set of deadlock markings. This can be done with an approach based on the computation of maximal implicit firing sequences enabled by the markings in the minimax-BRG. The approach we developed does not require the construction of the reachability graph and has wide applicability.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

A test generation framework for quiescent real-time systems

We present an extension of Tretmans theory and algorithm for test generation for input-output transition systems to real-time systems. Our treatment is based on an operational interpretation of the notion of quiescence in the context of real-time behaviour. This gives rise to a family of implementation relations parameterized by observation durations for quiescence. We define a nondeterministic (parameterized) test generation algorithm that generates test cases that are sound with respect to the corresponding implementation relation. Also, the test generation is exhaustive in the sense that for each non-conforming implementation a test case can be generated that detects the non-conformance

Analysis of Parameterized-Chain Networks: The Dependency Graph and Its Full, Consistent Subgraphs

This thesis studies algorithmic aspects of deadlock analysis for parameterized networks of discrete-event systems. A parameterized network consists of a finite, but arbitrarily large, number of interacting finite-state subsystems, each within one of a fixed, finite number of isomorphism classes. While deadlock analysis of such systems is generally undecidable, decidable subproblems have recently been identified. The decision procedure rests on the construction of a finite dependency graph for the network, and the computation of its full, consistent subgraphs. We present a software tool for such computations, and apply it to a train network example that extends beyond the current theoretical framework. The results suggest ways in which the framework could usefully be extended

Basis marking representation of Petri net reachability spaces and its application to the reachability problem

In this paper a compact representation of the reachability graph of a Petri net is proposed. The transition set of a Petri net is partitioned into the subsets of explicit and implicit transitions, in such a way that the subnet induced by implicit transitions does not contain directed cycles. The firing of implicit transitions can be abstracted so that the reachability set of the net can be completely characterized by a subset of reachable markings called basis makings. We show that to determine a max-cardinality-T_I basis partition is an NPhard problem, but a max-set-T_I basis partition can be determined in polynomial time. The generalized version of the marking reachability problem in a Petri net can be solved by a practically efficient algorithm based on the basis reachability graph. Finally this approach is further extended to unbounded nets

Discrete event approach to network fault management

Failure diagnosis in large and complex systems such as a communication network is a critical task. An important aspect of network management is fault management, i.e.,determining, locating, isolation, and correcting faults in the network. In the realm of discrete event systems Sampath et al proposed a failure diagnosis approach, and Jiang et al proposed an efficient algorithm for testing diagnosability. In this work, we adopt the framework of the communicating finite state machine (CFSM) of Miller et al for modeling networks and to investigate fault detection, fault identification and fault location using Sampath et al and Jiang et al methods. Our approach provides a systematic way of performing fault diagnosis aspects of network fault management